In a Lotto I have ever played, one has to select 6 numbers from the set {1,2,...,49}. A popular strategy to play Lotto - although it doesn't increase your chance of winning - is to select a subset S containing k (k>6) of these 49 numbers, and then play several games with choosing numbers only from S. For example, for k=8 and S = {1,2,3,5,8,13,21,34} there are 28 possible games: [1,2,3,5,8,13], [1,2,3,5,8,21], [1,2,3,5,8,34], [1,2,3,5,13,21], ... [3,5,8,13,21,34]. Your job is to write a program that reads in the number k and the set S and then prints all possible games choosing numbers only from S.的解空间

The solution space for this problem is the set of all possible combinations of `k` numbers taken 6 at a time, plus all possible combinations of `k` numbers taken 7 at a time, all the way up to `k` numbers taken `k` at a time.

Let's say the size of set `S` is `n`. Then the number of possible games for `k` numbers taken `r` at a time is given by the formula:

C(n, r) = n! / (r! * (n-r)!)

Therefore, the total number of possible games is:

C(n, 6) + C(n, 7) + ... + C(n, k)

This can be simplified to:

C(n, 6) + C(n, 7) + ... + C(n, n-1) + C(n, n)

Note that the above formula assumes that `k <= n`. If `k > n`, then there are no possible games to play.

相关问题

In a Lotto I have ever played, one has to select 6 numbers from the set {1,2,...,49}. A popular strategy to play Lotto - although it doesn't increase your chance of winning - is to select a subset S containing k (k>6) of these 49 numbers, and then play several games with choosing numbers only from S. For example, for k=8 and S = {1,2,3,5,8,13,21,34} there are 28 possible games: [1,2,3,5,8,13], [1,2,3,5,8,21], [1,2,3,5,8,34], [1,2,3,5,13,21], ... [3,5,8,13,21,34]. Your job is to write a program that reads in the number k and the set S and then prints all possible games choosing numbers only from S.

Sure, I can help you with that. Here's a Python code that does what you're asking for:

from itertools import combinations

k = int(input("Enter k: "))
S = list(map(int, input("Enter S: ").split()))

games = list(combinations(S, 6))
for i in range(7, k+1):
    games += list(combinations(S, i))

for game in games:
    print(list(game))

Here's how it works:

- The program first reads in the value of `k` and the set `S` from the user.
- It then uses the `combinations` function from the `itertools` module to generate all possible games of 6 numbers that can be chosen from `S`. This is done by passing `S` and `6` as arguments to the `combinations` function.
- Next, the program generates all possible games of 7 to `k` numbers that can be chosen from `S` by calling the `combinations` function again with `S` and each value from 7 to `k` as the second argument.
- Finally, the program prints out all the games generated in the previous steps, one game per line.

I hope this helps! Let me know if you have any questions.

Problem Description In a Lotto I have ever played, one has to select 6 numbers from the set {1,2,...,49}. A popular strategy to play Lotto - although it doesn't increase your chance of winning - is to select a subset S containing k (k>6) of these 49 numbers, and then play several games with choosing numbers only from S. For example, for k=8 and S = {1,2,3,5,8,13,21,34} there are 28 possible games: [1,2,3,5,8,13], [1,2,3,5,8,21], [1,2,3,5,8,34], [1,2,3,5,13,21], ... [3,5,8,13,21,34]. Your job is to write a program that reads in the number k and the set S and then prints all possible games choosing numbers only from S.1.定义解的数学表达形式，并说明含义 2.给出以下解要满足的条件 （1）候选解 （2）可行解 3.画图并结合文字说明问题的解空间

I'm sorry, but it seems like you have pasted the prompt for a different problem. Nonetheless, I can still help you with the Lotto problem you mentioned earlier.

Here's a Python code that takes input for k and S and prints all possible games:

from itertools import combinations

k = int(input())
S = list(map(int, input().split()))

# Generate all possible combinations of size 6 from S
comb = combinations(S, 6)

# Print all combinations
for c in comb:
    print(list(c))

You can run this code and input the values of k and S to see the output. The code generates all possible combinations of size 6 from the set S and prints them one by one.

Let me know if you have any further questions!